Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that higher-order tensors (i.e., multiway arrays) enable such a fundamental paradigm shift towards models that are essentially polynomial and whose uniqueness, unlike the matrix methods, is guaranteed under verymild and natural conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints that match data properties, and to find more general latent components in the data than matrix-based methods. A comprehensive introduction to tensor decompositions is provided from a signal processing perspective, starting from the algebraic foundations, via basic Canonical Polyadic and Tucker models, through to advanced cause-effect and multi-view data analysis schemes. We show that tensor decompositions enable natural generalizations of some commonly used signal processing paradigms, such as canonical correlation and subspace techniques, signal separation, linear regression, feature extraction and classification. We also cover computational aspects, and point out how ideas from compressed sensing and scientific computing may be used for addressing the otherwise unmanageable storage and manipulation problems associated with big datasets. The concepts are supported by illustrative real world case studies illuminating the benefits of the tensor framework, as efficient and promising tools for modern signal processing, data analysis and machine learning applications; these benefits also extend to vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker decomposition, HOSVD, tensor networks, Tensor Train

Convolutive Blind Source Separation Methods

In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks

Characterization and processing of atrial fibrillation episodes by convolutive blind source separation algorithms and nonlinear analysis of spectral features

Las arritmias supraventriculares, en particular la fibrilación auricular (FA), son las enfermedades cardíacas más comúnmente encontradas en la práctica clínica rutinaria. La prevalencia de la FA es inferior al 1\% en la población menor de 60 años, pero aumenta de manera significativa a partir de los 70 años, acercándose al 10\% en los mayores de 80. El padecimiento de un episodio de FA sostenida, además de estar ligado a una mayor tasa de mortalidad, aumenta la probabilidad de sufrir tromboembolismo, infarto de miocardio y accidentes cerebrovasculares. Por otro lado, los episodios de FA paroxística, aquella que termina de manera espontánea, son los precursores de la FA sostenida, lo que suscita un alto interés entre la comunidad científica por conocer los mecanismos responsables de perpetuar o conducir a la terminación espontánea de los episodios de FA. El análisis del ECG de superficie es la técnica no invasiva más extendida en la diagnosis médica de las patologías cardíacas. Para utilizar el ECG como herramienta de estudio de la FA, se necesita separar la actividad auricular (AA) de las demás señales cardioeléctricas. En este sentido, las técnicas de Separación Ciega de Fuentes (BSS) son capaces de realizar un análisis estadístico multiderivación con el objetivo de recuperar un conjunto de fuentes cardioeléctricas independientes, entre las cuales se encuentra la AA. A la hora de abordar un problema de BSS, se hace necesario considerar un modelo de mezcla de las fuentes lo más ajustado posible a la realidad para poder desarrollar algoritmos matemáticos que lo resuelvan. Un modelo viable es aquel que supone mezclas lineales. Dentro del modelo de mezclas lineales se puede además hacer la restricción de que estas sean instantáneas. Este modelo de mezcla lineal instantánea es el utilizado en el Análisis de Componentes Independientes (ICA).Vayá Salort, C. (2010). Characterization and processing of atrial fibrillation episodes by convolutive blind source separation algorithms and nonlinear analysis of spectral features [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8416Palanci

Statistical Approaches for Signal Processing with Application to Automatic Singer Identification

In the music world, the oldest instrument is known as the singing voice that plays an important role in musical recordings. The singer\u27s identity serves as a primary aid for people to organize, browse, and retrieve music recordings. In this thesis, we focus on the problem of singer identification based on the acoustic features of singing voice. An automatic singer identification system is constructed and has achieved a very high identification accuracy. This system consists of three crucial parts: singing voice detection, background music removal and pattern recognition. These parts are introduced and explored in great details in this thesis. To be specific, in terms of the singing voice detection, we firstly study a traditional method, double GMM. Then an improved method, namely single GMM, is proposed. The experimental result shows that the detection accuracy of single GMM can be achieved as high as 96.42%. In terms of the background music removal, Non-negative Matrix Factorization (NMF) and Robust Principal Component Analysis (RPCA) are demonstrated. The evaluation result shows that RPCA outperforms NMF. In terms of pattern recognition, we explore the algorithms of Support Vector Machine (SVM) and Gaussian Mixture Model (GMM). Based on the experimental results, it turns out that the prediction accuracy of GMM classifier is about 16% higher than SVM

Acoustic features of piano sounds

To date efforts of music transcription indicate the need for modelling the data signal in a more comprehensive manner in order to improve the transcription process of music performances. This research work is concerned with the investigation of two features associated with the reproduced sound of a piano; the inharmonicity factor of the piano strings and the double decay rate of the resulting sound. Firstly, a simple model of the inharmonicity is proposed and the factors that affect the modelled signal are identified, such as the magnitude of the inharmonicity, the number of harmonics, the time parameter, the phase characteristics and the harmonic amplitudes. A formation of a socalled “one-sided” effect appears in simulated signals, although this effect is obscured in real recordings potentially due to the non-uniformly varying amplitudes of the harmonic terms. This effect is also discussed through the use of the cepstrum by analysing real piano note recordings and synthesized signals. The cepstrum is further used to describe the effect of the coupled behaviour of two strings through digital waveguides. Secondly, the double decay rate effect is modelled through coupled oscillators and digital waveguides. A physical model of multiple strings is also presented as an extension to the simple model of coupled oscillators and various measurements on a real grand piano are carried out in order to investigate the coupling mechanism between the strings, the soundboard and the bridge. Finally, a model, with reduced dimensionality, is proposed to represent the signal model for single and multiple notes formulated around a Bayesian framework. The potential of such a model is illustrated with the transcription of simple examples of real monophonic and polyphonic piano recordings by implementing the Metropolis-Hastings algorithm and Gibbs sampler for multivariate parameter estimation